A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. There are 115 boxes in all. If the truck is carrying a total of 4525 pounds in boxes, how many of each type of box is it carrying?
Question
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. There are 115 boxes in all. If the truck is carrying a total of 4525 pounds in boxes, how many of each type of box is it carrying?
Solution
Let's denote the number of large boxes as L and the number of small boxes as S.
From the problem, we have two equations based on the total number of boxes and the total weight.
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L + S = 115 (This is because the total number of boxes is 115)
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55L + 25S = 4525 (This is because the total weight of the boxes is 4525 pounds, with each large box weighing 55 pounds and each small box weighing 25 pounds)
We can solve these equations simultaneously to find the values of L and S.
Let's start by multiplying the first equation by 25:
25L + 25S = 2875
Now, subtract this new equation from the second equation:
55L + 25S - (25L + 25S) = 4525 - 2875
This simplifies to:
30L = 1650
Divide both sides by 30 to solve for L:
L = 1650 / 30 = 55
Substitute L = 55 into the first equation:
55 + S = 115
Subtract 55 from both sides to solve for S:
S = 115 - 55 = 60
So, the truck is carrying 55 large boxes and 60 small boxes.
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